E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Lath or Lathe.
A division of a county. Sometimes it was an intermediate division between a hundred and a shire, as the lathes of Kent and rapes of Sussex, each of which contained three or four hundreds apiece. In Ireland the arrangement was different. The
officer over a lath was called a lathreeve. (Anglo-Saxon læth, a canton.)
If all that tything failed, then all that lath was charged for that tything; and if the lath failed, then all that hundred was demanded for them [i.e. turbulent fellows], and if the hundred, then the shire.Spenser: Ireland.